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Why numbering should start at zero (1982)
To denote the subsequence of natural numbers 2, 3, ..., 12 without the pernicious three dots, four conventions are open to us
Most cited
Posts that commenters keep linking to, ranked by how many different people have cited them in Hacker News comments. 77 posts.
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Nearly all binary searches and mergesorts are broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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On the Navier–Stokes Millennium Prize Problem
We’re sharing an AI-generated solution to the Navier–Stokes Millennium Prize Problem, including a writeup and a formal proof in Lean.
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Nearly all binary search and merge sort implementations are broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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Consistency Models
Jepsen analyzes the safety properties of distributed systems–most notably, identifying violations of consistency models. But what are consistency models? What phenomena do they allow? What kind of consistency does a given program really need?
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Learning to Reason with LLMs
We are introducing OpenAI o1, a new large language model trained with reinforcement learning to perform complex reasoning. o1 thinks before it answers—it can produce a long internal chain of thought before responding to the user.
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Programming with Nothing (2011)
I love Ruby! I’ve used it every day for years and I’m not sick of it yet. It’s an easy language to love: it’s expressive, flexible and syntactically beautiful ; it has a unique combination of useful features like mixins , metaclasses and blocks ; it comes with a useful core library and comprehensive standard library …
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AI solves International Math Olympiad problems at silver medal level
Breakthrough models AlphaProof and AlphaGeometry 2 solve advanced reasoning problems in mathematics
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Nearly All Binary Searches and Mergesorts Are Broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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Announcing the first SHA-1 collision
Posted by Marc Stevens (CWI Amsterdam), Elie Bursztein (Google), Pierre Karpman (CWI Amsterdam), Ange Albertini (Google), Yarik Markov (Goog...
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An OpenAI model has disproved a central conjecture in discrete geometry
An OpenAI model solved the 80-year-old unit distance problem, disproving a major conjecture in discrete geometry and marking a milestone in AI-driven mathematics.
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A Mathematical Framework for Transformer Circuits (2021)
Transformer language models are an emerging technology that is gaining increasingly broad real-world use, for example in systems like GPT-3 , LaMDA , Codex , Meena , Gopher , and similar models. However, as these models scale, their open-endedness and high capacity creates an increasing scope for unexpected and…
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Backblaze Releases the Reed-Solomon Java Library for Free
Today we are releasing our latest open-source project: Backblaze Reed-Solomon Java library for erasure coding. Click for details on how to use and download.
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The Superinvestors of Graham-and-Doddsville (1984)
Columbia Business School. For over 100 years, we’ve helped develop leaders who create value for business and society at large.
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Rationality: From AI to Zombies
A series by Eliezer Yudkowsky
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On Vigna's PCG Critique
On 14 May 2018, Sebastiano Vigna added a page to his website (archived here) entitled “The wrap-up on PCG generators” that attempts to persuade readers to avoid various PCG generators. That day, he al
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Schelling's Model of Segregation
Racial segregation has always been a pernicious social problem in the United States. Many factors have contributed to segregation including prejudice, zoning laws, housing discrimination, and loan discrimination. Although much effort has been extended to desegregate our schools, churches, and neighborhoods, the US…
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Evolution Strategies as a Scalable Alternative to Reinforcement Learning
Stay up to speed on the rapid advancement of AI technology and the benefits it offers to humanity.
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Learning more about Claude's mathematical capabilities
An unreleased Claude model improved the lower bound for the fraction of zeroes of the Riemann zeta function that satisfy the hypothesis, raising it from 41.6% to 67.2%.
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Efficiently Generating a Number in a Range
The vast majority of my posts about random number generation have focused on looking at the properties of different generation schemes. But, perhaps surprisingly, the performance of your randomized a
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The algebra and calculus of algebraic data types
Just as algebra is fundamental to the whole of mathematics, algebraic data types (ADTs) are fundamental to many common functional programming languages. They’re the primitives upon which all of our richer data structures are built, including everything from sets, maps, and queues, to bloom filters and neural networks .
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Nearly all binary searches and mergesorts are broken (2006)
Posted by Joshua Bloch, Software EngineerI remember vividly Jon Bentley's first Algorithms lecture at CMU, where he asked all of us incoming Ph.D. ...
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Eytzinger Binary Search
This tutorial is loosely based on a 46-page paper by Paul-Virak Khuong and Pat Morin “Array layouts for comparison-based searching” and describes one particular way of performing efficient binary search by rearranging elements of a sorted array in a cache-friendly way.
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AlphaGeometry: An Olympiad-level AI system for geometry
Our AI system surpasses the state-of-the-art approach for geometry problems, advancing AI reasoning in mathematics